To determine whether each relation represents a
function, we use the
definition of a function:
> A
relation is a
function if
each input (x-value) in the domain is paired with
exactly one output (y-value) in the range.
> That means:
No input can map to more than one output.
We will examine each mapping diagram and check if any input (left side) has
more than one arrow pointing to different outputs (right side).
---
1)
- Inputs: -1, 0, 4, 7, 8, 12, 13
- Outputs: -6, -2, 5, 6, 8, 17
Check each input:
- -1 → -6
✔
- 0 → -2
✔
- 4 → 5
✔
- 7 → 6
✔
- 8 → 8
✔
- 12 → 17
✔
- 13 → 8
✔
Each input maps to
only one output.
✔ Yes, this is a function.
---
2)
- Inputs: -19, -14, -11, -9, 2, 4
- Outputs: -16, -13, -11, -9, 9, 10
Check:
- -19 → -16
✔
- -14 → -13
✔
- -11 → -11
✔
- -9 → -9
✔
- 2 → 9
✔
- 4 → 10
✔
Wait — look at
-9: it points to
-9 and also to
-13? Let's trace:
- -9 → -9
✔
- Also, -9 → -13? Yes! There’s an arrow from -9 to -13.
So
-9 maps to two outputs: -9 and -13.
✘ Not a function (one input maps to two outputs).
---
3)
- Inputs: -5, -2, 0, 3, 6, 7
- Outputs: 10, 11, 14, 15, 17, 19
Check:
- -5 → 10
✔
- -2 → 11
✔
- 0 → 14
✔
- 3 → 15
✔
- 6 → 17
✔
- 7 → 19
✔
All inputs go to only one output.
✔ Yes, this is a function.
---
4)
- Inputs: 4, 5, 7, 10, 11, 12, 15
- Outputs: 1, 3, 4, 8, 9
Check:
- 4 → 1
✔
- 5 → 3
✔
- 7 → 4
✔
- 10 → 8
✔
- 11 → 9
✔
- 12 → 9
✔
- 15 → 1
✔
Now, check for duplicates:
- 12 → 9
- 11 → 9 → both go to 9 — that's fine.
Multiple inputs can go to same output.
- But no input goes to multiple outputs.
So all inputs have
only one arrow.
✔ Yes, this is a function.
---
5)
- Inputs: -19, -18, -16, -14, -12, -10, -8
- Outputs: -20, -14, -12, -11, -10, -7, -4
Check:
- -19 → -20
✔
- -18 → -14
✔
- -16 → -12
✔
- -14 → -11
✔
- -12 → -10
✔
- -10 → -7
✔
- -8 → -4
✔
Each input has exactly one output.
✔ Yes, this is a function.
---
6)
- Inputs: -7, -5, 0, 1, 5, 10, 14
- Outputs: -11, 1, 4, 5, 17
Check:
- -7 → -11
✔
- -5 → 1
✔
- 0 → 4
✔
- 1 → 5
✔
- 5 → 17
✔
- 10 → 1
✔
- 14 → 1
✔
Now, check for multiple outputs per input:
- Each input has only
one arrow.
- Even though multiple inputs (like -5, 10, 14) go to
1, that's allowed.
✔ Yes, this is a function.
---
✔ Final Answers:
1)
Yes
2)
No (because -9 maps to both -9 and -13)
3)
Yes
4)
Yes
5)
Yes
6)
Yes
---
Summary:
| Problem | Is it a Function? |
|--------|-------------------|
| 1 | Yes |
| 2 | No |
| 3 | Yes |
| 4 | Yes |
| 5 | Yes |
| 6 | Yes |
Let me know if you'd like these explained further or need them written on the worksheet format!
Parent Tip: Review the logic above to help your child master the concept of function mapping worksheet.
